Constructing Benney reductions associated with cyclic \((n,s)\) curves

DOI10.1007/BF03321881zbMath1244.14020MaRDI QIDQ766036

John Gibbons

Publication date: 22 March 2012

Published in: Computational Methods and Function Theory (Search for Journal in Brave)

Full work available at URL: http://www.heldermann.de/CMF/CMF11/CMF112/cmf11036.htm

zbMATH Keywords

algebraic curvesalgebraic computationAbelian functionsSchwartz-Christoffel mappingdispersionless integrable systemsprime form

Mathematics Subject Classification ID

Jacobians, Prym varieties (14H40) Relationships between algebraic curves and integrable systems (14H70) Special divisors on curves (gonality, Brill-Noether theory) (14H51) Theta functions and curves; Schottky problem (14H42) Symbolic computation of special functions (Gosper and Zeilberger algorithms, etc.) (33F10)

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The Gibbons–Tsarev equation: symmetries, invariant solutions, and applications

Cites Work

• The Benney hierarchy and the Dirichlet boundary problem in two dimensions
• Double pendulum and \(\theta\)-divisor
• On directional derivatives of the theta function along its divisor
• Conformal maps and reductions of the Benney equations
• Reductions of the Benney equations.
• Higher genus hyperelliptic reductions of the Benney equations
• Hyperelliptic reduction of the Benney moment equations
• The initial value problem for reductions of the Benney equations
• Genus 4 trigonal reduction of the Benney equations
• Genus-Nalgebraic reductions of the Benney hierarchy within a Schottky model
• Tata lectures on theta. II: Jacobian theta functions and differential equations. With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman, and H. Umemura